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Abstract

Discretization and linearization of the steady-state Navier-Stokes equations
gives rise to a nonsymmetric indefinite linear system of equations. In this
paper, we introduce preconditioning techniques for such systems with the
property that the eigenvalues of the preconditioned matrices are bounded
independently of the mesh size used in the discretization. We confirm and
supplement these analytic results with a series of numerical experiments
indicating that Krylov subspace iterative methods for nonsymmetric systems
display rates of convergence that are independent of the mesh parameter.
In addition, we show that preconditioning costs can be kept small by
using iterative methods for some intermediate steps performed by the
preconditioner.
(Also cross-referenced as UMIACS-TR-94-66)